Hybrid Tree Automata and the Yield Theorem for Constituent Tree Automata

Constituency Parsing as an Instance of the M-monoid Parsing Problem

“…This problem has been solved on the grammar side by exploring more powerful grammar formalisms such as tree adjoining grammars (TAG; [7]) and linear context-free rewriting systems (LCFRS; [15,8]). On the automaton side, hybrid tree automata [2] have recently been introduced. In this context, hybrid trees are usual trees where labels can be extended by a positive number, called index, which indicates their position in the phrase.…”

“…We briefly recall the automaton model of [2]. In essence, a hybrid tree automaton (HTA) is an FTA where each transition additionally has an index constraint which describes the acceptable combinations VP → (VP, (x 1 1 x 1 2 x 2 1 ))(V, ADV)…”

“…It is discontinuous as the phrase of the left subtree is interleaved with a word from the right subtree. Center: formalization of this constituent tree in the framework of [2]. Right: AST of an RTG and its evaluation in the algebras of our M-monoid parsing problem.…”

“…If unrestricted, these general constraints lead to an overly expressive automaton model. This is why [2] also introduced constituent tree automata (CTA) as a restricted form of HTA to recognize languages of constituent trees. Here, the index constraints are given by word tuples as they occur in LCFRS.…”

“…Our first contribution is the instantiation of the M-monoid parsing problem to constituency parsing. In attempting this instantiation, the constituent trees by [2] turn out to be not suitable for such an algebraic framework. Instead, we introduce partitioned constituent trees which are inspired by Nederhof and Vogler (2014) [14] (also cf.…”